SUMS OF DUAL TOEPLITZ PRODUCTS ON THE ORTHOGONAL COMPLEMENTS OF FOCK-SOBOLEV SPACES

doi:10.1007/s10473-024-0302-0

Acta mathematica scientia,Series B ›› 2024, Vol. 44 ›› Issue (3): 810-822.doi: 10.1007/s10473-024-0302-0

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SUMS OF DUAL TOEPLITZ PRODUCTS ON THE ORTHOGONAL COMPLEMENTS OF FOCK-SOBOLEV SPACES

Yong CHEN¹, Young Joo LEE^2,*

1. Department of Mathematics, Hangzhou Normal University, Hangzhou 311121, China;
2. Department of Mathematics, Chonnam National University, Gwangju 61186, Korea

Received:2022-09-06 Revised:2023-01-08 Online:2024-06-25 Published:2024-05-21
Contact: *E-mail:leeyj@chonnam.ac.kr
About author:E-mail: ychen@hznu.edu.cn
Supported by:
Chen's research was supported by the NSFC (12271134, 11771401); Lee's research was supported by the Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (NRF-2019R1I1A3A01041943).

Abstract

Abstract: We consider dual Toeplitz operators on the orthogonal complements of the ock-Sobolev spaces of all nonnegative real orders. First, for symbols in a certain class containing all bounded functions, we study the problem of when an operator which is finite sums of the dual Toeplitz products is compact or zero. Next, for bounded symbols, we construct a symbol map and exhibit a short exact sequence associated with the $C^*$-algebra generated by all dual Toeplitz operators with bounded symbols.

Key words: dual Toeplitz operators, Fock-Sobolev spaces, symbol map

CLC Number:

47B35

Yong CHEN, Young Joo LEE. SUMS OF DUAL TOEPLITZ PRODUCTS ON THE ORTHOGONAL COMPLEMENTS OF FOCK-SOBOLEV SPACES[J].Acta mathematica scientia,Series B, 2024, 44(3): 810-822.

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SUMS OF DUAL TOEPLITZ PRODUCTS ON THE ORTHOGONAL COMPLEMENTS OF FOCK-SOBOLEV SPACES

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